If the witch catches you, she will turn you into a gingerbread man and add you to her collection outside her house.
If you are outside, invisibility ring and the protection spell will keep the witch from catching you. If you walk inside the witch's house, invisibility ring will stop working. It appears that while under the protection spell, the witch is never inside her house.
The witch is easy enough to avoid, but you will need some items inside her house. So, it is not a bad idea to rid Daventry of the witch. Find out more about the Witch's House.
The old King was said to have saved a Princess from a pack of wolves. It turned out the princess actually was a witch, who took his Magic Chest and left. Perhaps this is the witch.
For some reason, I hated this old hag from the beginning and usually the first thing I do it get rid of her. (Maybe it's payback for what the witch in Hero's Quest I put me though).